Transition Mechanisms Attendant to Large Amplitude Parametric Vibrations of Rectangular Plates

1967 ◽  
Vol 89 (4) ◽  
pp. 619-625 ◽  
Author(s):  
J. H. Somerset
Keyword(s):  
Rectangular Plate ◽  
Large Amplitude ◽  
Strong Influence ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Parametric Vibrations ◽  
Periodic Load ◽  
Simply Supported ◽  
Stochastic Loading ◽  
Parametric Oscillations

Experiments have been conducted to investigate the transition mechanisms attendant to the parametric vibrations of a simply supported rectangular plate subjected to a periodic load of the form P = P0 + P1 cos γt. It is found that the transition mechanisms, such as “jumps” within the zone and “dropout” from the zone, are influenced by the initial curvature of the plate and by interactions with the source of energy. Due to the possibility of transitions between the parametric oscillations and forced vibrations of the plate, “splitting” of the zone may occur. Preliminary experiments indicate that the transition mechanisms have a strong influence on the response of the plate to stochastic loading.

Buckling of Rectangular Plates With General Variation in Thickness

1973 ◽  
Vol 40 (3) ◽  
pp. 745-751 ◽  
Author(s):  
D. S. Chehil ◽  
S. S. Dua
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Perturbation Technique ◽  
Thickness Variation ◽  
Rectangular Plates ◽  
Bending Vibration ◽  
Simply Supported ◽  
Buckling Stress ◽  
General Variation ◽  
Plate Of Variable Thickness

A perturbation technique is employed to determine the critical buckling stress of a simply supported rectangular plate of variable thickness. The differential equation is derived for a general thickness variation. The problem of bending, vibration, buckling, and that of dynamic stability of a variable thickness plate can be deduced from this equation. The problem of buckling of a rectangular plate with simply supported edges and having general variation in thickness in one direction is considered in detail. The solution is presented in a form such as can be easily adopted for computing critical buckling stress, once the thickness variation is known. The numerical values obtained from the present analysis are in excellent agreement with the published results.

Forced Vibrations of Thin, Elastic, Rectangular Plates with Edges Elastically Restrained Against Rotation

1977 ◽  
Vol 21 (01) ◽  
pp. 24-29
Author(s):  
E. A. Susemihl ◽  
P. A. A. Laura
Keyword(s):  
Bending Moment ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Edge Conditions ◽  
Approach Infinity ◽  
Square Plate ◽  
Elastic Rectangular Plate ◽  
Elastically Restrained ◽  
The Galerkin Method

Polynomial coordinate functions and the Galerkin method are used to determine the response of a thin, elastic, rectangular plate with edges elastically restrained against rotation and subjected to sinusoidal excitation. It is shown that when the flexibility coefficients approach infinity (simply supported edge conditions) the calculated results practically coincide with the exact solution in the case of a square plate when four terms of the expansion are used. Dynamic displacement and bending moment amplitudes are tabulated for different length-to-width ratios, flexibility coefficients, and frequency values.

Fundamental Frequency of Simply Supported Rectangular Plates With Linearly Varying Thickness

1965 ◽  
Vol 32 (1) ◽  
pp. 163-168 ◽  
Author(s):  
F. C. Appl ◽  
N. R. Byers
Keyword(s):  
Rectangular Plate ◽  
Fundamental Frequency ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Varying Thickness

Upper and lower bounds for the fundamental eigenvalue (frequency) of a simply supported rectangular plate with linearly varying thickness are given for several taper ratios and plan geometries. These bounds were determined using a previously published method which yields convergent bounds. In the present study, all results have been obtained to within 0.5 percent maximum possible error.

Stability of Rectangular Plates Under Shear and Bending Forces

1936 ◽  
Vol 3 (4) ◽  
pp. A131-A135 ◽  
Author(s):  
Stewart Way
Keyword(s):  
Critical Load ◽  
Rectangular Plate ◽  
Bending Moment ◽  
The Other ◽  
Rectangular Plates ◽  
Bending Stress ◽  
Simply Supported ◽  
Tension And Compression ◽  
The Way

Abstract The author first discusses the problem of a plane, simply supported rectangular plate loaded by shearing forces in the plane of the plate on all four edges. There are two stiffeners attached one third and two thirds of the way along the plate. The critical load is calculated for various stiffener rigidities. Also, the rigidity necessary to keep the stiffeners straight when the plate buckles is found. This stiffener rigidity is found to be slightly larger than that necessary for a plate with one stiffener and the same panel dimensions as the plate with two stiffeners. The second problem discussed by the author is that of a plane, simply supported rectangular plate loaded by uniformly distributed edge shearing forces in the plane of the plate and linearly distributed tension and compression in the plane of the plate at the ends. The end forces vary from tension hσo, at one corner to—hσo, at the other corner, so that their resultant is a bending moment. The presence of the edge shearing forces is found to diminish the critical bending stress in this case. Calculations are made for various magnitudes of bending and shearing forces for plates of various proportions.

Response of Beams and Plates to Random Loads

1957 ◽  
Vol 24 (1) ◽  
pp. 46-52
Author(s):  
A. C. Eringen
Keyword(s):  
Cross Correlation ◽  
External Pressure ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Probable Number ◽  
Simply Supported ◽  
Random Loads ◽  
Stochastic Loading ◽  
Special Cases ◽  
The Cross

Abstract With the use of generalized harmonic analysis the problem of vibrating damped beams and plates under stochastic loading is solved. The resulting equations give the cross-correlation functions for displacements, stresses, moments, and so on, in terms of the cross-correlation function of external pressure. Mean square values of these functions are special cases of these results. Using a method due to Rice, we also calculate the probable number of times per unit time the random displacements or stresses will exceed a given value. The case of simply supported bars, cantilever bars, clamped circular plates, and simply supported rectangular plates are worked out in detail.

Solving the Deflection Equations of Thick Plate under Concentrated Load

2012 ◽  
Vol 594-597 ◽  
pp. 2659-2663
Author(s):  
Dan Zhang
Keyword(s):  
Rectangular Plate ◽  
Thick Plate ◽  
Numerical Results ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
Concentrated Load ◽  
Simply Supported ◽  
Thick Rectangular Plate ◽  
Reciprocal Theorem Method

According to reciprocal-theorem method (RTM), the deflection equations of thick rectangular plate with two edges simply supported and two edges free under concentrated load are obtained in this paper. Simultaneously through the programming computation, the numerical results with actual value are obtained, which further showed the accuracy and superiority of RTM to solve the bending of thick rectangular plates.

Free Vibration of Rectangular Plates Stiffened With Viscoelastic Beams

1985 ◽  
Vol 52 (2) ◽  
pp. 397-401 ◽  
Author(s):  
K. Ohtomi
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Convenient Method ◽  
Laplace Transformation ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Rectangular Plates ◽  
Dirac Delta ◽  
Simply Supported ◽  
Delta Functions

This investigation treats the free vibration of a simply supported rectangular plate, stiffened with viscoelastic beams. Using a convenient method in which the effects of beams are expressed with Dirac delta functions, the equation of motion can be expressed by only one equation. The frequency equation is obtained by applying the Laplace transformation to the equation of motion. The effects of the volume and the number of beams on the frequency and the logarithmic decrement are clarified.

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